Question

The hourly demand for music downloads is given by:

Q^d = 25 – 5P,

            where Q^d is the number of songs demanded per hour, and P is the price of downloading a song. 

Suppose that P = $3. At this price, what does the price elasticity of demand equal? What is the total revenue?

At what price does ε = 1? What is the total revenue when the price is $2.50?

Explain whether your results to part a and part b are consistent with the Total Revenue Test.

 

Answer 1

a)

elasticity of demand= slope of demand curve x P/Q

slope of demand curve=-5

$P=\$ 3$

$Q_d=25-5P$

$= 25-5(3)$

$=10$

elasticity of demand $=-5\times \frac{3}{10}$

$=-1.5$

b)

Total revenue is given by;

$P\times Q$

$P=\$3$

$Q_d=25-5P$

$= 25-5(3)$

$=10$

$Revenue=3\times 10$

$=\$30$

c)

The elasticity of demand= slope of demand curve x P/Q

PED=1

$1=5\times \frac {P}{Q}$

$\frac {P}{Q}=\frac {3}{10}$

$=0.3$

$\frac{P}{Q}=\frac{P}{25-5P}$

$0.3=\frac {P}{25-{5P}}$

$P=0.3(25-5P)$

$P=7.5-1.5P$

$P+1.5P=7.5$

$P=3$

Thus PED=1 when the price is $3

d)

Revenue= P X Q

When P=$2.5 Q will be:

$Q=25-5P$

$=25-5(2.5)$

$=12.5$

$2.5\times 12.5 =\$ 31.25$

e)

They are consistent with the total revenue test since a fall in price is leading to a rise in total revenue in the presence of elastic demand.

when the price falls from $3 to $2.5 the total revenue rises from $30 to $31.25. This is in line with the revenue test.

When a decrease in price causes an increase in total revenue, demand can be said to have been elastic since an increase in price has a greater impact on the quantity demanded.